1. Field of the Invention
The present invention relates generally to systems and techniques for modeling and characterizing printed-circuit board wiring, and particularly, to an improved system and method for generating more accurate transmission line models and characterizations for predicting performance of circuits and circuit structures as printed-circuit board transmission data-rates increase.
2. Description of the Prior Art
There currently exists limited techniques for providing time and frequency domain measurements from which transmission line models and material parameters for characterizing high frequency performance of printed-circuit board (PCB) conductor structures (i.e., transmission lines) may be extracted.
One particular technique, known in the art as short-pulse-propagation, SPP, is a time-domain technique that may be employed to model and characterize performance of circuits and circuit structures. As described in the reference to A. Deutsch, R. S. Krabbenhoft, et al. entitled “Practical Considerations in the Modeling and Characterization of Printed-Circuit Board Wiring”, Digest of SPI'06, Signal Propagation on Interconnects, May 10-13, 2006, Berlin, pp. 1-4, incorporated by reference herein, the SPP technique requires propagating a short, electrical pulse along two identical transmission lines with different lengths, l1 and l2. In current practice, the short pulse is generated by differentiating the step-source of a sampling oscilloscope.
FIG. 1 depicts an exemplary prior art measurement apparatus 10 for characterizing high frequency performance of a non-production level (test) PCB showing a short pulse generating source 12 feeding test pulse signals to coaxial probes 16 for differential measurement. The prior art set-up depicted in FIG. 1 is a bench-test set-up configured to conduct a time domain transmission (TDT) measurement technique by launching a short, electrical pulse onto a transmission-line structure on the PCB and measuring the pulse signals to compute characterizing data. In one embodiment, using the test set-up 10 shown in FIG. 1, the test pulse signals are obtained by differentiating the step-source of a sampling oscilloscope 12 (e.g., an HP model 54120A) using a passive impulse-forming network 17. In one embodiment, source pulses are, for example, 35 ps and 29 ps (obtained with the Picosecond Pulse Labs pulse generator 4015C and the 5208 network) width and are launched on respective transmission-line structures of different line lengths via test pads formed on the surface of the PCB. High-speed coaxial probes 16 in ground-signal (GS) configuration, (GGB Industries model 40A, 15OLP) are used to connect to the transmission-lines via test pads. In FIG. 1, a 50-GHz sampling oscilloscope 12 uses a detector channel, e.g., with 2.4 mm connectors and 40 GHz flexible coaxial cables 19 (e.g., Gore GD/AJ, 160-mil-diameter) between the probes 16 and the oscilloscope 15.
Although not shown in FIG. 1, the test set-up 10 is further configured to provide at the PCB a parallel-plate device by which a low-frequency capacitance measurement may be made by a low frequency impedance analyzer. More particularly, according to the prior art, the line self and mutual capacitances are able to be measured and modeled, e.g., at 1 MHz as is the effective dielectric constant of region around the lines.
In accordance with the SPP technique using the apparatus depicted in FIG. 1, the transmitted pulses are detected and digitized. A time window technique is applied to the pulses to eliminate unwanted reflections from the measurement probes, any contact pads and vias, and cable connectors. In exemplary embodiments, a rectangular time window is used with a smooth transition to the signal baseline steady-state level since the amplitude resolution is more essential than the spectral resolution for this technique. A Fast Fourier Transform (FFT) is performed on the processed waveforms to obtain the complex propagation constant Γ(f) set forth in equation (1):
                              Γ          ⁡                      (            f            )                          =                                            α              ⁡                              (                f                )                                      +                          j              ⁢                                                          ⁢                              β                ⁡                                  (                  f                  )                                                              =                                                    1                                                      l                    1                                    -                                      l                    2                                                              ⁢                              ln                ⁡                                  (                                                                                    A                        1                                            ⁡                                              (                        f                        )                                                                                                            A                        2                                            ⁡                                              (                        f                        )                                                                              )                                                      +                          j              ⁢                                                                                          Φ                      1                                        ⁡                                          (                      f                      )                                                        -                                                            Φ                      2                                        ⁡                                          (                      f                      )                                                                                                            l                    1                                    -                                      l                    2                                                                                                          (        1        )            where α(f) and β(f) are the attenuation and phase constant, respectively, of the transmission line as a function of frequency (f), and, Ai(f) and Φi(f) are the respective amplitude and the phase of the transforms corresponding to the lines with lengths of l1 and l2 and l1>l2. As referred to herein, frequency is referred to as a variable “f” or “ω”.
From the ratio of the two Fourier transforms, the broadband attenuation and phase constant is extracted. No de-embedding or calibration is needed as in frequency-domain based techniques using Vector-Network Analyzers, VNA. The per-unit-length R(f), L(f), C(f), G(f) parameters (R is resistance, L is inductance, C is capacitance, and G is conductance) for the transmission line structure are then calculated using the dimensions obtained by cross sectioning the PCB hardware. This calculation is performed by using an (electromagnetic) field solver that also requires the metal resistivity information of the T-line structures. This metal resistivity information is obtained in accordance with equation (2) by performing a four-point resistance measurement of the two lines and using the actual dimensions,
                    R        =                              ρ            ⁢                                                  ⁢            l                    A                                    (        2        )            where R is the resistance of the conductor and p is the resistivity, l is the length and A the cross-sectional area of the T-line conductor.
The initial calculation of the per-unit-length R(f), L(f), C(f), G(f) parameters for the transmission line structure is performed with an initial estimation of dielectric constant and dielectric loss. For the low frequency range of 10 KHz to 1 MHz, actual measurements of dielectric loss can be made on a large parallel plate structure embedded on the same PCB structure with the signal layer of interest.
The dielectric constant “∈” at 1 MHz can be reliably measured from the capacitance measurement on the parallel plate structure of the PCB in accordance with equation (3):
                    C        =                                            ɛ              0                        ⁢                          ɛ              r                        ⁢            A                    h                                    (        3        )            where C is the capacitance, ∈r the relative permittivity, ∈o the absolute permittivity, A the plate area, and h is the thickness of the dielectric. In current practice, for the signal transmission frequency range between 1 GHz to 50 GHz, an initial guess is made. An electromagnetic field solver is implemented to fit a range of values for the complex permittivity using this initial guess. The attenuation and phase are then calculated based on the R, L, C, G values. The calculated and measured values are compared, and, the procedure is repeated until good agreement is obtained. Each time, the dielectric loss is changed.
The field solver generates causal results for C(f) and G(f) based on a Debye model for the complex permittivity:
                              ɛ          ⁡                      (            ω            )                          =                              ɛ            ∞                    +                                    ∑              i                        ⁢                                          ɛ                i                                            1                +                                  j                  ⁢                                                                          ⁢                  ω                  ⁢                                                                          ⁢                                      τ                    i                                                                                                          (        4        )            where ∈i ∈∞ and τi are parameters or the expansion in accordance with the Debye model.
The final C(f) and G(f) are used, together with the measured ∈r and the calculated C at 1 MHz, to obtain a measure of the broadband complex permittivity in accordance with equations (5).
                                                        ɛ              r                        ⁡                          (              ω              )                                =                                    (                                                C                  ⁡                                      (                    ω                    )                                                                    C                                      1                    ⁢                                                                                  ⁢                    MHz                                                              )                        ×                          ɛ                              r                ⁢                                                                  ⁢                1                ⁢                                                                  ⁢                MHz                                                    ⁢                                  ⁢                              tan            ⁢                                                  ⁢                          δ              ⁡                              (                ω                )                                              =                                    G              ⁡                              (                ω                )                                                    ω              ⁢                                                          ⁢                              C                ⁡                                  (                  ω                  )                                                                                        (        5        )            where ω is the frequency and tan δ a measure of dielectric loss.
The broadband characteristic impedance Zo is now obtained from equation (6):
                              Z          0                =                              Γ            ⁡                          (              ω              )                                                          G              ⁡                              (                ω                )                                      +                          j              ⁢                                                          ⁢              ω              ⁢                                                          ⁢                              C                ⁡                                  (                  ω                  )                                                                                        (        6        )            
It is the case that typical VNA based measurements can generally obtain attenuation and phase, especially for high frequency range, but Zo(f) cannot be extracted due to the large discontinuities found in realistic multi-layer printed-circuit-boards, PCBs. As was demonstrated in the reference to T-M. Winkel, et al., entitled, “Comparison of Time- and Frequency-Domain Measurement Results for Product Related Card and MCM Transmission Lines up to 65 GHz”, Proc. Dig. IEEE 14th Top. Mtg Elec. Perf. of Electronic Packaging, Austin, Tex., Oct. 24-26, 2005, pp. 21-24, the current de-embedding and calibration techniques cannot compensate for the large end effects, i.e., the capacitance, resistance, inductance of the via, test pads, and probes.
As data rates transmitted on printed-circuit-boards increase from 2 Gbps to 20 Gbps and beyond, there is required more accurate and causal transmission line models for predicting system performance. Non-causal models can cause inaccurate signal integrity and timing prediction and simulator convergence problem. In order to generate broadband causal models (DC to ˜50 GHz) there is needed higher accuracy and higher-bandwidth measurements of dielectric constant ∈r(f) and dielectric loss tan δ(f). Single value ∈r and tan δ that are typically supplied by vendors cannot generate causal models. The current practice for monitoring the integrity of production level printed-circuit boards is to measure the Zo obtained from TDR measurements using a single, hand-held probe. One such prior art probe for TDR measurements is a hand-held probe 80 provided by Polar Instruments Ltd. (Beaverton Oreg.) such as depicted in FIG. 8A with its cover removed. In this embodiment, a Polar generated step source for conducting the TDR measurement has an approximate 120 ps-200 ps rise-time. Additionally, a 10 mil pitch coaxial probe 85 additionally shown in FIG. 7A can also be used for high-speed measurements as these types of coaxial probes may generate 1 ps-35 ps transitions. Further, the hand-held probes 80 include the probe tips 87 depicted in FIG. 7B with a 100 mil pitch as shown in close-up view.
Thus, currently, ∈r and tan δ values are generally supplied only at a few frequencies and measured on simple, non-representative structures. However, it is the case that such measurements are required to be made on multi-layer configurations and the data is needed over a wide frequency range such as from DC to 50 GHz. In addition, as higher-performance systems need the development of lower loss materials, these new materials need to be analyzed in representative, multi-layer structures. Furthermore, concerns to be considered such as losses due to roughness that could become significant, in the order of 5-50% loss increase at 5 GHz, for example. Further considerations to be accounted for include: moisture absorption of new materials that impacts reliability. Further, lead-free compatibility imposes manufacturing constraints that impact electrical characteristics.
Moreover, simple TDR production-level Zo process monitors need to be improved because such techniques overpredict Zo due to losses on the board wiring. Overprediction of Zo affects board design, cost, wireability, and system power. Thus, Zo extraction needs to be extended to broadband phase constant Γ(f) and broadband characteristic impedance Zo(f).
It would be highly desirable to provide an improved test apparatus that can extend this measurement capability to multi-layer production level PCB boards by providing at least two lines of different lengths and utilizing better probes, improved structures, and instrumentation.
It is desired that such improved testability further maintain the ruggedness commensurate with production level testing.